Alternative approach to thermodynamic phase transitions

One of the major open problems in theoretical physics is the lack of a consistent quantum gravity theory. Recent developments in our knowledge on thermodynamic phase transitions of black holes and their van der Waals-like behavior may provide an interesting quantum interpretation of classical gravity. Studying different methods of investigating phase transitions can extend our understanding of the nature of quantum gravity. In this paper, we present an alternative theoretical approach for finding thermodynamic phase transitions in the extended phase space. Unlike the standard methods based on the usual equation of state involving temperature, our approach uses a new quasi-equation constructed from the slope of temperature versus entropy. This approach addresses some of the shortcomings of the other methods and provides a simple and powerful way of studying the critical behavior of a thermodynamical system. Among the applications of this approach, we emphasize the analytical demonstration of possible phase transition points and the identification of the non-physical range of horizon radii for black holes.